acf_supIG: Autocorrelation function of the supIG trawl function
Description
This function computes the autocorrelation function associated with the supIG
trawl function.
Usage
acf_supIG(x, delta, gamma)
Arguments
x
The argument (lag) at which the autocorrelation function associated
with the supIG trawl function will be evaluated
delta
parameter in the supIG trawl
gamma
parameter in the supIG trawl
Value
The autocorrelation function of the supIG trawl function evaluated at
x
Details
The trawl function is parametrised by the two parameters \(\delta
\geq 0\) and \(\gamma \geq 0\) as follows: $$g(x) =
(1-2x\gamma^{-2})^{-1/2}\exp(\delta \gamma(1-(1-2x\gamma^{-2})^{1/2})),
\mbox{ for } x \le 0.$$ It is assumed that \(\delta\) and \(\gamma\) are
not simultaneously equal to zero. Its autocorrelation function is given by:
$$r(x) = \exp(\delta\gamma (1-\sqrt{1+2 x/\gamma^2})), \mbox{ for } x
\ge 0.$$